Mathematics

A daring speculation offers a potential way forward in one of the great unsolved problems of mathematics: the behavior of the Navier-Stokes equations for fluid flow.

Improvements in how densely spheres and other shapes can be packed together could lead to advances in materials science, deep space communication and theoretical physics.

By investigating the central role played by knots in fluids and fields, physicists hope to unravel long-standing mysteries of turbulence.

To determine the nature of infinity, mathematicians face a choice between two new logical axioms. What they decide could help shape the future of mathematical truth.

Working on the centuries-old twin primes conjecture, two solitary researchers and a massive collaboration have made enormous advances over the last six months.

Scientific data sets are becoming more dynamic, requiring new mathematical techniques on par with the invention of calculus.

Physicists have discovered a jewel-shaped geometric object that challenges the notion that space and time are fundamental constituents of nature.

Two young mathematicians are illuminating a frontier in the study of rational solutions to polynomial equations: the cubics.

A virtually unknown researcher has made a great advance in one of mathematics’ oldest problems, the twin primes conjecture.